Complex exponential expressions.

I just need some kind of explanation in layman's terms of what exactly is going on here. It seems as though I am missing some key element from trig. I am in a Signals class and the book lacks an explanation of the reduction used and ultimately why.

Staff: Mentor

I just need some kind of explanation in layman's terms of what exactly is going on here. It seems as though I am missing some key element from trig. I am in a Signals class and the book lacks an explanation of the reduction used and ultimately why.

Ok, so in "b": I do not understand the simplification or reduction to the side, where 4pi is added. Also I think the same method occurs in the third answer of "d".

What they're doing in b is adding multiples of 2##\pi## so as to get a positive angle.

From Euler's formula, eix = cos(x) + i*sin(x). This represents a complex number whose magnitude is 1, and that makes an angle of x radians measured counterclockwise from the positive Real axis. Note that mathematicians use i for the imaginary unit, and engineers use j.

Adding 2##\pi## or multiples of 2##\pi## to the exponent to get ei(x + 2##\pi##) doesn't change anything except the angle. This complex number still has a magnitude of 1 - the only difference is that the angle is now x + 2##\pi##, which gets you to exactly the same point on the unit circle.